Free Printable Chapter 1 Review - The Real Number System & Operations

1.

Identify the following number: $\sqrt[]{5}$

a)

Rational

b)

Irrational

2.

Select all RATIONAL numbers

a)

4.5

b)

5

c)

$\sqrt[]{47}$

d)

0

e)

$\pi$

3.

Select all IRRATIONAL numbers

a)

45.6635482...

b)

4

c)

-4.2

d)

$\frac{4}{3}$

e)

$\sqrt[]{34}$

4.

Classify the following: $\sqrt[]{13}$

a)

Rational

b)

Irrational

5.

Select the complete classification for the following number:

75

a)

real, rational

b)

real, rational, integer, whole

c)

real, rational, integer, whole, natural

d)

real, irrational

6.

Select the complete classification for the following number: $\sqrt[]{10}$

a)

real, rational

b)

real, rational, integer

c)

real, rational, integer, whole

d)

real, irrational

7.

Which number is irrational?

a)

$1.\overline{89}$

b)

$\frac{1}{2}$

c)

1.3459206739451...

8.

TRUE OR FALSE: -1.5 is rational

a)

TRUE

b)

FALSE

9.

-12 + 9

a)

21

b)

3

c)

-3

d)

-21

10.

18 + (-4)

a)

-14

b)

22

c)

14

d)

-22

11.

19 - (-19)

a)

0

b)

36

c)

26

d)

38

12.

-7 - (-2) = ?

a)

9

b)

-9

c)

-5

d)

5

13.

A mountain was 50 feet below sea level. Over time, the height increased 75 feet. How high is the mountain now?

a)

25 feet

b)

-125 feet

c)

-25 feet

d)

-125 feet

14.

Bob lost 5 points on page one of his math test and he lost 9 points on page two of his math test. Which equation best describes Bob progress on his math test?

a)

5 + 9 = 14

b)

-5 + -9 = -4

c)

-5 + -9 = -14

d)

5 + -9 = -4

15.

What is the value of -16 / 8?

a)

0.5

b)

2

c)

-0.5

d)

-2

16.

What is the value of -54 / -9?

a)

7

b)

6

c)

-6

d)

-8

17.

What is the value of (-12) * 4

a)

-48

b)

48

c)

-3

d)

3

18.

Which is ALWAYS true?

a)

a negative TIMES a negative is negative

b)

a negative TIMES a positive is negative

c)

a negative PLUS a positive is negative

d)

a positive MINUS a negative is negative

19.

Identify each true statement. (Hint: there are 3)

a)

(-27) / (-3) = 9

b)

10 - (-4) = -14

c)

(-9) - 5 = -4

d)

4 * (-7) = -28

e)

(-12) + 13 = 1

20.

The value of x * y will be...

a)

positive, because one value is negative and one is positive

b)

negative, because both values are negative

c)

positive, because both values are positive

d)

negative, because one value is negative and one is positive

21.

Barbara loses 5 points every time she forgets her homework. What integer represents the change in her grade if she forgets her homework 4 times?

a)

-5

b)

5

c)

-20

d)

20

22.

There are __?__ significant digits in the number 23.012.

a)

1

b)

2

c)

4

d)

5

23.

There are __?__ significant digits in the number 0.00076

a)

2

b)

4

c)

5

d)

6

24.

There are __?__ significant digits in the number 2,000,000

a)

1

b)

2

c)

6

d)

7

25.

There are __?__ significant digits in the number 90,000.00

a)

1

b)

2

c)

5

d)

7

26.

Why is the zero significant in the digit 706?

a)

It is an ending zero after the decimal point.

b)

It is a beginning zero.

c)

It is between 2 significant digits.

d)

It is not a significant digit.

27.

Why is the 0 a significant digit in the number 15.92340?

a)

It is an ending zero after the decimal point.

b)

It is a beginning zero.

c)

It is between 2 significant digits.

d)

It is not a significant digit.

28.

Which is correct regarding the significant digits for the number 0.0054?

a)

The zeroes are not significant digits since they are beginning zeroes.

b)

The zeroes are not significant digits since they are ending zeroes.

c)

They are significant since they are between significant digits.

d)

All zeroes are not significant digits.

29.

Which of the following is the answer for the problem with the correct number of significant digits?
24.32 + 1.2 = 25.52

a)

25.6

b)

25.52

c)

25.5

d)

25

30.

Which of the following is the answer for the problem with the correct number of significant digits?
53 + 23.4 = 76.4

a)

77.0

b)

77

c)

76.4

d)

76

31.

Which of the following is the answer for the problem with the correct number of significant digits?
19.008 - 14.53 = 4.478

a)

5

b)

4.5

c)

4.48

d)

4

32.

Ted has 18 feet of lumber. How many 2 1/2 foot shelves can he make?

a)

7

b)

7 1/4

c)

7 1/5

d)

7 1/3

33.

What is the reciprocal of the number 2 2/3?

a)

8/3

b)

3/8

c)

4/7

d)

2/3

34.

Divide.
1 5/7 divided by 1 3/7

a)

1 1/5

b)

1 15/49

c)

2 15/49

d)

1 15/49

35.

What is the inverse operation of division?

a)

Multiplication

b)

Addition

c)

Subtraction

d)

Division

36.

A reciprocal is two numbers whose product is 1.

a)

True

b)

False

37.

solve

a)

- 2/9

b)

- 5/9

c)

2/9

d)

no there

38.

solve

a)

1 1/2

b)

- 1 5/9

c)

1 5/9

d)

not here

39.

a)

-6/12

b)

-5/12

c)

5/12

d)

-5/7

40.

Divide.

a)

-1/10

b)

-5/8

c)

-2/20

d)

5/8

41.

Multiply.

a)

-7 1/5

b)

-4/45

c)

-8

d)

7

42.

Which expression can also be used to calculate the expression above?

a)

b)

c)

d)

43.

A recipe for cookies requires 2/3 cup of butter. Rama wants to make 3/4 of the recipe. How many cups of butter should Rama use to make the cookies?

a)

b)

c)

d)

44.

When multiplying or dividing a NEGATIVE and NEGATIVE number your answer will be...

a)

Positive

b)

Negative

c)

Depends on the largest number

d)

None of the above

45.

When multiplying or dividing a NEGATIVE and POSITIVE number your result will be...

a)

Positive

b)

Negative

c)

Depends on which is bigger.

d)

None of the above

46.

Convert to a decimal
1/8

a)

.25

b)

.125

c)

.55....

d)

.18888...

47.

Convert to a decimal
3/4

a)

.25

b)

.34

c)

.75

d)

.44...

48.

What is the sum?
$\frac{4}{5}+\frac{1}{5}$

a)

^{$\frac{5}{10}$}

b)

^{$\frac{1}{2}$}

c)

1

d)

_{$\frac{4}{5}$}

49.

What is the product?
⁴/₅ × ¹/₅

a)

⁵/₁₀

b)

⁴/₁₀

c)

⁴/₂₅

d)

⁵/₂₅

50.

What is the quotient?
³/₄ ÷ ³/₈

a)

¹/₂

b)

¹/₄

c)

0

d)

2

51.

What is the difference?
⁹/₁₄ - ³/₇

a)

³/₁₄

b)

⁶/₇

c)

³/₁₄

d)

⁶/₁₄

52.

Will the answer be positive or negative?
-2 × (-5) × (-1) × (-9)

a)

Positive

b)

Negative

53.

Will the answer be positive or negative?
-2 + (-5) + (-1) + (-9)

a)

Positive

b)

Negative

54.

Select all operations with fractions that require a common denominator.

a)

addition

b)

division

c)

multiplication

d)

subtraction

55.

Perform the indicated operation.

1/8 + 3/8

Reduce, or simplify answer.

a)

4 / 8

b)

1 / 4

c)

4 / 16

d)

1 / 2

56.

Find the sum of

3/8 and 1/3.

Reduce, or simplify answer.

a)

4 / 11

b)

1 / 8

c)

17 / 24

d)

1 / 24

57.

Find the difference of

47 / 56 and 15 / 56.

Write answer in simplest form.

a)

16 / 28

b)

32 / 56

c)

4 / 7

d)

8 / 14

58.

Find the difference.

7/8 - 4/5

Reduce, or simplify answer.

a)

-1 / 40

b)

3 / 40

c)

3 / 8

d)

1

59.

When multiplying fractions, a common denominator is required.

a)

TRUE

b)

FALSE

60.

Perform the indicated operation.

(5/6) × (3/8)

Write answer in lowest terms.

a)

16 / 5

b)

48 / 15

c)

15 / 48

d)

5 / 16

61.

Find the product of

(1/6) and (2/3).

Reduce, or simplify answer.

a)

1 / 4

b)

9

c)

1 / 9

d)

3 / 12

62.

"Multiply by the reciprocal" is the rule for which operation with fractions?

a)

addition

b)

division

c)

multiplication

d)

subtraction

63.

Find the quotient of

(2/3) and (5/6) .

Reduce, or simplify.

a)

12 / 15

b)

5 / 9

c)

4 / 5

d)

-1 / 6

64.

2 ¼ ÷ 4 ⅕ =

a)

11/26

b)

⅝

c)

⅞

d)

15/28

65.

3 1/4 ÷ 3

a)

1 1/12

b)

3 4/3

c)

6 1/2

d)

2 1/2

66.

86.9 + 49.8

a)

136.5

b)

136.7

c)

136.9

d)

137.6

e)

137.7

67.

55.82 + 3.947

a)

59.767

b)

58.767

c)

57.787

d)

59.787

e)

58.787

68.

800.45 - 723.5

a)

76.55

b)

76.75

c)

76.95

d)

77.75

e)

77.95

69.

75 - 38.52

a)

36.52

b)

36.48

c)

37.52

d)

37.48

70.

9.7 x 8.6

a)

83.48

b)

83.72

c)

83.42

d)

72.48

e)

72.42

71.

24 x 0.008

a)

0.192

b)

1.632

c)

1.92

d)

0.1632

72.

4.97 ÷ 7 =

a)

7.01

b)

0.701

c)

0.71

d)

7.1

73.

0.576 ÷ 0.24

a)

0.24

b)

2.4

c)

2.31

d)

0.231

74.

Brad purchases M&Ms at Walmart. Each pack costs $0.79, and he gives the cashier $7.11. How many packs of M&Ms did Brad purchase?

a)

7

b)

8

c)

9

d)

11

75.

Kara is making copies of articles she needs to for her research paper. The local library charges $0.17 per page, and she has 55 pages to xerox. What will be the charges for her copies?

a)

$9.69

b)

$9.35

c)

$8.25

d)

$8.69

e)

$9.25

76.

Latoya purchased a movie ticket at Northwoods Cinema for $6.50. She also bought popcorn for $5.75, a soda for $5.25, and a box of Skittles for $3.75. How much money did she spend at Northwoods Cinema?

a)

$20.25

b)

$20.75

c)

$21.25

d)

$21.75

77.

My grandmother bought 10 yards of fabric at Walmart, and she used 7.508 yards to make a curtain for my bedroom window. She then used another 1.491 yards of the fabric to make a pillow case. How much fabric was left?

a)

2.001 yards

b)

1.999 yards

c)

1.508 yards

d)

1.491 yards

e)

1.001 yards

78.

3.86 × 2.97

a)

11.4642

b)

10.9296

c)

10.7694

d)

10.2672

79.

Solve the following:

-12 ÷ 6 (-3) + 8

a)

14

b)

2

c)

-22

d)

3

80.

Solve the following:
8 + (-4) ÷ 4

a)

-7

b)

1

c)

-1

d)

7

81.

Solve the following:
6(-3) - 2

a)

1

b)

-16

c)

-20

d)

20

82.

True or False?
2(-3) + 10 = 9

a)

True

b)

False

83.

Solve the following:
-5 (- 6) + 10

a)

-1

b)

40

c)

-20

d)

21

84.

Find and explain the error.
5 - 3 + 2
5 - 5
0

a)

There is no error.

b)

Addition was done first and you should have subtracted first

c)

There is a subtraction error

85.

True or False?
2 + (-6)2 = -10

a)

True

b)

False

86.

What are the steps to solve the following expression?
50 − 16 ÷ 2

a)

add, multiply

b)

subtract, divide

c)

divide, subtract

d)

subtract, multiply

87.

Solve the following:
3 + 27 ÷ (-3)

a)

-6

b)

-10

c)

10

d)

-12

88.

Solve the following:
25 ÷ 5 × 3 – 3

a)

12

b)

2

c)

0

d)

300

89.

What would be the 2nd step in solving this problem:
-12 ÷ 6 + -3 ∘ 7

a)

multiplication

b)

subtraction

c)

addition

d)

division

90.

Solve the following:
-14 ÷ 2 – 15

a)

-8

b)

-22

c)

8

d)

22

91.

What would be my first step in solving this problem?
3 + 4 ∗ 6 - 4

a)

addition

b)

multiplication

c)

subtraction

d)

exponents

92.

2 + (9²- 4)

a)

16

b)

77

c)

79

93.

2 ÷ 1 + 2 + 9 ÷ 9

a)

13/9

b)

5

c)

1 1/3

d)

13

94.

2 ÷ 1 + 2 + 9 ÷ 9

a)

13/9

b)

5

c)

1 1/3

d)

13

95.

Simplify the following:
-8 + (15 - 3) ÷ 4

a)

-5

b)

1

c)

-11

d)

11

96.

Solve the following:
-8 + (15-3) ÷ 4

a)

-5

b)

1

c)

-11

d)

11

97.

6 + (4)3

a)

18

b)

30

c)

13

d)

42

98.

4(8) ÷ (8 − 6)

a)

-2

b)

18

c)

-1

d)

16

99.

Solve the following:
(2 + 7 - 1) ÷ 2²

a)

16

b)

2

c)

72.25

d)

8.75

100.

(7 + 41) ÷ 2 – 15

a)

19

b)

9

c)

25

d)

3

101.

Simplify the following:
5 - 6² ÷ 4 - 3

a)

1

b)

-10.75

c)

-31

d)

-7

102.

10 + 45 ÷ 9 -(14 ÷ 2) =

a)

9

b)

7

c)

53

d)

18

103.

40 - 2⁴ + 8

a)

40

b)

32

c)

24

d)

42

104.

2 + (9²- 4)

a)

16

b)

77

c)

79

d)

88

105.

2² + 3²x (7+1)

a)

77

b)

76

c)

78

d)

79

106.

Simplify the following:
-2 ⋅ (3 + 8 ÷ 4)²

a)

-16

b)

1.375

c)

4

d)

-50

107.

90 - 5² x 3

a)

15

b)

240

c)

195

108.

(82 ÷ 2) × 3 – 17

a)

206

b)

100

c)

106

d)

5

109.

-7(10)=

a)

70

b)

700

c)

-70

d)

-700

110.

-3(-4)

a)

-12

b)

7

c)

-7

d)

12

111.

-7 + (-4) =

a)

-3

b)

11

c)

-11

d)

-3

112.

-2 - (-8)

a)

6

b)

-6

c)

-10

d)

10

113.

0 - 16

a)

16

b)

0

c)

-16

d)

5

114.

-10+4

a)

-14

b)

14

c)

-6

d)

6

115.

-20+(-11)

a)

31

b)

9

c)

-9

d)

-31

116.

-12 + 9

a)

21

b)

3

c)

-3

d)

-21

117.

-9 + 9

a)

18

b)

-18

c)

0

d)

81

118.

Find and explain the error.
5 - 3 + 2
5 - 5
0

a)

There is no error.

b)

Addition was done first and you should have subtracted first

c)

There is a subtraction error

119.

Solve the following:
5 - 6² ÷ 4 - 3

a)

1

b)

-10.75

c)

-31

d)

-7

120.

Solve the following:
91 + 27 ÷ (72 ÷ 24)

a)

100

b)

96

c)

90

d)

127

121.

4 + [5² + (-4 - 1)] ÷ 10

a)

2.4

b)

4

c)

6

d)

7

122.

(2 + 7 - 1) ÷ 2²

a)

16

b)

2

c)

72.25

d)

8.75

123.

5 - 6² ÷ 4 - 3

a)

1

b)

-10.75

c)

-31

d)

-7

124.

Which operation must be performed first?
5² + (9 - 1) ÷ 4 × 10 + 1

a)

5²

b)

9 - 1

c)

4 × 10

d)

10 + 1

125.

True or False:
5(-2) - 3 = -7

a)

True

b)

False

126.

(-2) × 4 - 3²

a)

-17

b)

1

c)

-1

d)

17

127.

True or false: all addition must be simplified before any subtraction

a)

True

b)

False

128.

-8(2 - 5) ÷ (-4)

a)

-6

b)

6

c)

8

d)

-8

Chapter 1 Review - The Real Number System & Operations

Total questions: 128

Worksheet time: 7hrs 14mins

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